A396220 Number of relations R on an n-element set such that the transitive closure of R has exactly eight elements more than R.

0, 0, 0, 0, 4719, 3183890, 1078414245

Offset

0,5

Comments

Equivalently, a(n) is the number of binary relations R on an n-set for which exactly eight ordered pairs must be adjoined to obtain a transitive relation; i.e., |closure(R) \ R| = 8.

Links

Table of n, a(n) for n=0..6.

Example

For n <= 3 we have n^2 <= 9, so a relation differing from its closure by eight pairs would have to be empty with full closure, which is impossible. Hence a(0) = a(1) = a(2) = a(3) = 0.

Crossrefs

Cf. A006905, A395083, A395919, A395920, A396053, A396054, A396055.

Sequence in context: A107544 A092375 A252239 * A234086 A093789 A357607

Adjacent sequences: A396217 A396218 A396219 * A396221 A396222 A396223

Keyword

nonn,hard,more

Author

Firdous Ahmad Mala, May 19 2026

Status

approved